Question

The resultant of two equal forces is equal to either of these forces. The angle between them is

• A. $\frac{\mathrm{\pi }}{4}$
• B. $\frac{\mathrm{\pi }}{3}$
• C. $\frac{\mathrm{\pi }}{2}$
• D. $\frac{2\mathrm{\pi }}{3}$

Answer 1

The correct option is D

$\frac{2\mathrm{\pi }}{3}$

Step 1: Given data

$Resultantforce\left(R\right)=Firstforce\left(F_1\right)=Secondforce\left(F_2\right)$

Step 2: Formula used

The following formula can be used to compute the resultant force between two vectors.

$R=\sqrt{F_1^2+F_2^2+2F_1{F}_2\cos \theta }$

Step 3: Compute the angle

It is understood that $R=F_1=F_2$. So,

Substitute $R$ in the formula in place of $F_1$ and $F_2$ in the formula,

$R=\sqrt{R^2+R^2+2R^2\cos \theta }$

Take the square of both sides,

$\begin{array}{rcl}{R}^2& =& 2R^2+2R^2\cos \theta \\ R^2& =& 2R^2\left(1+\cos \theta \right)\\ \frac{1}{2}& =& 1+\cos \theta \\ \cos \theta & =& -\frac{1}{2}\\ \theta & =& {120}^{°}\end{array}$

Thus, the angle between them is $\frac{2\mathrm{\pi }}{3}$.

Hence, option D is the correct answer.